Let $\Omega \subset \mathbf{R}^{N}$ be an open bounded set with a Lipschitz boundary and let $g: \Omega \times \mathbf{R} \to \mathbf{R}$ be a Carathéodory function satisfying usual growth assumptions. Then the functional $$\Phi(u) = \int_{\Omega} g(x,u(x)) \, dx$$ is lower semicontinuous with respect to the weak topology on $W^{1,p}(\Omega)$, $1 \le p \le \infty$, if and only if $g$ is convex in the second variable for almost every $x \in \Omega$.